Most of the assumptions in Condition REF  are classical assumptions (or generalizations thereof), e.g. [1]}, [2]}, [3]}, made for the analysis of variational methods.
The major difference in the analysis provided here is that \(\mathcal {R}\)  is relatively sub-differentiable, which we have motivated in Section , and the assumption that in general the regularized solutions are not global minima but only \(\phi \) -critical points.
